My epiphany regarding loudspeaker construction happened one evening when I
was listening to music loud enough to shake the walls, floor, and everything
else in the room. When the cone of a loudspeaker driver (see a cut-away
drawing of a driver, 8.2 kb) vibrates back and forth to produce sound, energy
flows from the front of the cone into the room; but an equal amount of energy
flows from the back of the cone through the arms of the frame and into
the speaker enclosure (at low frequencies the load seen by the back is different
than the front, so this is not really true at all frequencies). If that amount
of energy can shake a floor made with 3/4" plywood over 2"x8" floor joists on
16" centers, no wonder it will make a speaker cabinet vibrate. We will come
back to why cabinet vibrations are problematic after a few paragraphs. (Note:
in this section "cabinet" and "enclosure" are used interchangeably).

Two good sources of information that I learned a lot from are The Loudspeaker Design Cookbook, by Vance Dickason (see references), and Lynn Olson's web site. An additional nice source of information is snippets.

A tutorial which discusses damping of panel vibrations and the importance of
enclosure sound absorption is provided at E-A-R
online. Specialty products for these applications are discussed as well.

Raison d'être for a speaker enclosure

A primary function of a speaker enclosure is to keep the sound coming from
the back of a driver cone from going into the room. The sound from the back
of a driver is 180 degrees out of phase with
the sound from the front. For bass frequencies the sound from the back would
cancel the sound from the front, destroying the low frequency performance. At
higher frequencies where the wavelength
is smaller than the driver diameter, the situation is more complex. The sound
may add, cancel, or something in between. The sound from the back is also delayed
in time by a fraction of a millisecond, which can interfere with the stereo
imaging (see discussion on source location).
Preventing all sound from the backs of all drivers from going into the room
is by far the cleanest way to obviate these problems. I chose this approach.
Other approaches, which can (and do) produce good-sounding loudspeakers, are
discussed in the section on system
design. There is also an excellent description of various design approaches
by Dickason. One method for eliminating sound from the back would be to mount
a driver in a wall. The sounds from the front and the back of the driver cone
can then freely radiate in opposite directions into two different open spaces,
or at least large spaces, and never the twain shall meet. This is known as an
"infinite baffle," and a closed box enclosure design that attempts to approximate
this situation is called an infinite baffle enclosure. Such an enclosure is
ideally air-tight. Small leaks can make noises, and in designs using small enclosures,
leaks will also alter the intended behavior of the enclosure. When the sound
going into the enclosure vibrates the cabinet walls, the walls will radiate
sound back into the room. In addition to combining with the front radiation
in odd and unpredictable ways, sound radiating from the cabinet walls will have
a weird frequency response. In particular, the walls will respond especially
strongly at a number of resonant frequencies. The enclosure walls will also
ring like a bell once they start to vibrate at these resonances, messing up
the transient response. The cabinet walls are not the only things that can ring
like a bell. Internal reflections within the cabinet can set up standing waves
that also create resonances at certain frequencies. Sound at these frequencies
can pass back through the speaker cone into the room, even if the enclosure
walls are perfectly rigid.

All drivers should have their own individual enclosures. If a woofer and midrange
share the same enclosure, when the woofer is pumping back and forth with a big
bass note, the pressure it creates inside the enclosure will push the midrange
back and forth, and can push it into a non-linear
region. Finally, the geometry of the cabinet should allow the sound from all
drivers to combine in a way that results in a smooth frequency response, good
transient response, and with minimum diffraction.
(A lot more on this below). So, to summarize, the objectives of speaker construction
are to create an enclosure that:

is air-tight

has walls that do not vibrate a lot

does not have strong internal resonances

isolates each driver from the others

has a geometry compatible with good sound reproduction

The air-tight part is relatively easy: just brace,
glue and screw all joints (6.2 kb), and then caulk everything thoroughly.
Use a high quality caulk that will remain flexible, so it doesn't develop cracks.

The internal resonance part is also pretty easy: just fill the cabinet with
fiberglass, and bye-bye resonances. Some people worry about the enclosure dimensions,
but fiberglass is so effective that the dimensions are really irrelevant. Note
that empty non-rectangular enclosures resonate just as badly as rectangular
ones, despite what many people think. In this regard, at various times spherical
speakers have been hyped as eliminating or minimizing internal resonances. A
comparison of the resonant frequencies of a spherical and cubical cavity of
equal volumes are shown in this figure
[42kb]. The cavities are quite large, but the frequencies simply scale up for
smaller enclosures. The sphere has a sparser set of resonances, but the behavior
is not all that different. For the derivation of these resonances see Resonances
in a Spherical Cavity.

I built a cabinet within a cabinet to isolate the drivers, as shown in the
photograph taken during the enclosure construction
(69 kb). This also has the beneficial side-effect that essentially no sound
coming from the back of the midrange makes it into the room, since it mainly
has to pass through two enclosures. The tweeter has its own tiny little enclosure
(not shown). The large woofer enclosure is 6' x 3' x 2'. The walls are 1-1/8"
thick. It weighs a lot. I actually had to rig up
a block and tackle (30 kb photo) to move it around during construction!

The really hard objective is obtaining nearly vibration-free walls,
which brings us back to all that energy flowing into the enclosure. This, and
geometry issues, are the subject of the remainder of this section.

My epiphany gave me a new appreciation of the sheer power I was dealing with, and I also realized that the energy going into the enclosure has to go somewhere. A basic law of physics, conservation of energy, says that energy doesn't just disappear. In the case of the speaker enclosure, there are only two things that can happen to the energy flowing into the enclosure: (1) sound energy can flow back out into the room, or (2) the sound energy can be converted into heat by sound absorbing material. Some books on speaker construction emphasize bracing the walls up the kazoo to make them rigid. Suppose we could make them infinitely rigid. No energy can be coupled into an infinitely rigid wall. If there were no sound absorbing materials inside the enclosure, basic physics says that the sound energy escapes the only way it can: back through the speaker cone into the room. This is clearly a bad outcome. The most important characteristic of an enclosure is its internal sound absorbing capability. Fortunately, fiberglass is cheap, and filling the cabinet to the brim with fiberglass creates a very effective sound sponge.

I tested a lot of schemes for reducing panel vibration. The
drawing of the basic experimental setup (12.9 kb) shows the new large (black)
speaker enclosure, but constructed at this point as a completely closed box
with no openings for the drivers. The top panel was gasketed and secured with
56 bolts. Inside the large box was an old (red) loudspeaker. An acoustic guitar
pickup was attached to the top panel and connected to my CLIO
system. The experiments involved firing up the speaker inside the box and recording
the response of the guitar pickup, which picks up the vibrations of the top
panel. I also listened. The first time I played fairly loud music through the
speaker inside the otherwise empty box was a real revelation. The large box
at this point was sturdily constructed out of 3/4" medium density fiberboard
(MDF); it was a complete sieve for the sound. It was just amazing. Of
course, this is just physics at work. As noted above, the sound energy had no
place to go except to escape the box (actually, the panels do absorb some sound
energy as heat, but apparently not a lot). The CLIO system was used to drive
the old speaker through an amp, and to record the vibrations sensed by the acoustic
pickup. Various configurations were tested for the top panel where the pickup
was attached. Typical of the designs I tested is the one shown in the illustration
of a "constrained layer" (7.6 kb) of damping material. The constrained layer
technique is well known to vibration control specialists (see Nashif, et al.
in references), but seems to be surprisingly under-utilized
in the audio community. Dickason discusses the technique in his book, and mentions
a few commercial designs where it was employed. If designed correctly, according
to Nashif, it is the most effective technique for vibration damping. Incredibly,
despite this "prior art," Sony Corporation was granted a patent #05949033 on
the technique Sept 7, 1999. A graph of the responses
(50 kb) from five of my experiments reveals several interesting results. The
horizontal axis in the graph is frequency, in Hz. The vertical scale is the
output from the acoustic guitar pickup, in dB. (The curves have smoothed a bit
using a running average in frequency). I have no idea what the frequency response
of the guitar pickup is, and we are mainly interested in relative levels anyway,
but it was a real surprise to me that the vibrations appear to peak at 2000
Hz, and are significant to 4000 Hz and higher. I had expected the response would
be highest at low frequencies and essentially disappear above a few hundred
Hz. The red curve was the first test, where the inside of the large enclosure
was empty (except for the old loudspeaker), and the top was 3/4" MDF. The blue
curve represents the same configuration except that the interior was filled
about 50% with fiberglass (the garden-variety type used to insulate houses).
The fiberglass filling reduces the panel vibration by about 20 dB across the
entire frequency range. This corresponds to absorbing 99% of the sound energy,
at a very low cost, and with very little effort. And it kills internal standing
waves. The lesson here is real clear: stuff the enclosure with fiberglass.
All remaining tests included the fiberglass filling. The black curve is for
3/4" MDF plus a layer of 1/4" tempered Masonite, but no damping layer. I was
again surprised that adding this layer didn't improve things more than it did,
but this was probably because the two layers were only attached at the edges
by the array of bolts. If the two layers had been glued together I think there
would be more improvement. The final two curves are for the full sandwich with
the damping layer. The damping layer for the cyan curve is 1/8" loaded vinyl
that costs $2.00 per square foot. The damping layer for the green curve is 2
layers of 30# roofing felt that costs $0.17 per square foot (thanks to Dickason
for mentioning this stuff). The constrained layer of roofing felt reduces the
peak vibration by almost 20 dB, and the average by about 10 dB, relative to
the blue curve without a damping layer. In most regions it is better than the
hi-tech pricey vinyl. Needless to say, I chose the roofing felt sandwich for
my enclosure construction.

Notes added 9/14/99 in response to several questions (which are always welcome).
I did not use any adhesive on the damping layer. It was clamped around the edge
with screws. My gut feeling is that a good adhesive would make an improvement.
However I was concerned about aging (i.e. the adhesive becoming stiff), and
I was also reluctant to test any adhesive, since if it didn't work, I was really
"stuck." I did try putting a lot of screws more or less randomly in the middle,
which made things worse. Finally, it worked pretty well just in there loose,
and "if it ain't broke, don't fix it." If anyone else has experience and wants
to share, I will be happy to post it here (with full credit of course). The
basic structure of the box was 3/4-inch MDF braced with 2x2s at the corners.
Drivers were directly attached to this structure. The damping sandwich was layered
on top of all panels inside the box, but stopped short of butting against the
interior braces, by about 1/4 inch. More 2x2 bracing was added on all panels,
on roughly 1-foot centers. Sometimes this bracing was on the outside of the
MDF, sometimes on the inside on top of the damping layer. (If they wouldn't
show, they went outside).

Note added 12/31/2006: W. Wilgus writes that there is a 3M product called Schutz,
gunk for damping automotive panels, that is a good material for damping enclosure
walls. Another note added 6/25/2007. Phil Walusek notes that, strictly speaking,
the technique I use is not constrained layer damping since I didn't use adhesive.
He also referred me to two sites, SP
Technology, and a pdf document within the E-A-R site referenced above, specifically
on the topic of constrained
layer damping.

Most books on loudspeaker construction really emphasize bracing. What I found is that bracing helps only at the lowest frequencies, below 100 Hz. Another result that really surprised me is that when the cabinet vibrates, the whole thing vibrates. I had expected the panels to exhibit modal resonance patterns. Specifically, at the corners I expected the vibration to be quite low. Not so. All of my expectations were true at certain specific frequencies, but sweeping over the full frequency band shows remarkably similar behavior, regardless of where the pickup is located. This is not to say that bracing should not be used. In fact, I liberally used 2"x2" braces. But don't expect braces to eliminate vibration, and be aware that damping is a lot more effective than bracing.

While we are on the subject of vibrations, the enclosure can also couple vibrations
into the floor, creating another spurious sound source and degrading soundproofing.
Setting the speaker on the floor on spikes was very popular when this was originally
written, and maybe still is. Personally, I think this is mainly hype, although
a speaker that is prone to rocking back and forth on thick carpeting probably
does benefit from spikes. I used heavy vinyl tubing as an isolation mount. It
is difficult for me to pin down exactly how effective this is, but it appears
to work OK. A nice discussion regarding spikes vs. damping material, including
measurements, is included in the Sonic
Design web page. The conclusion is that spikes are not good, creating distortion
among other things. I recently had an e-mail informing me that roofing felt
under the speaker helps as well.

A major goal of this project was to achieve near-perfect time-alignment. The reason for this is to obtain near-perfect transient response. As shown in the section on final system measurements, the result actually achieved was excellent. The illustration on time-alignment (5.5 kb) shows the driver geometry. If all drivers are mounted flush on a flat vertical panel, with the tweeter near the elevation of your ears, the sound from the tweeter will reach your ears about 0.1 millisecond before the sound from the midrange. Not only does this mess up the transient response, it can mess up the frequency response in the crossover region. In order to time-align the drivers, the front panel face is terraced as shown in the illustration. The amount of horizontal offset of each driver was determined by measurements with the CLIO system. The vertical spacing between the midrange and tweeter should be as small as possible to minimize lobing. The CLIO measurements and lobing are discussed in a separate and somewhat more technical subsection. The same subsection contains a comparison of lobing with a "D'Appolito array" configuration and the tweeter/midrange geometry I use. Although the D'Appolito has a lesser degree of lobing, as long as I sit in my design "sweet spot," there is really no advantage gained for the additional complexity. I also learned - too late - that if the midrange was above the tweeter the useful size of the "sweet spot" would be about the same as the D'Appolitio array. Some speaker manufacturers obtain a horizontal offset between drivers by tilting the front panel backwards. In this case, the drivers point toward the ceiling, and the listening position is at an angle from the pointing direction. The frequency response of a driver is different, and usually worse, away from the pointing direction. Also, the reflections from the ceiling are stronger when the drivers point upward. For these reasons I did not like this design and created the terraced design instead. There are other designs that maintain a straight-ahead pointing direction for the drivers, but, as far as I know, the terracing design I came up with is original. The terracing did lead to a tricky design problem regarding diffraction, which is covered in the following subsection.

See an animated cartoon on diffraction (107
kb. last time I tried this it worked with Firefox and Internet Explorer, but
not with Netscape). Diffraction from the front panel and cabinet edges can have
a bad effect on stereo imaging because the time-delays of the diffracted sound
are more often than not right in the critical region for direction sensing (see
discussion on source location). When
I did my initial measurements on my tweeter, I measured it mounted flush with
the face of the test panel, and mounted with the rim extended about 1/4" above
the surface, as illustrated in the cartoon. I was surprised (this project was
full of surprises) at how much this changed the frequency response. Without
flush-mounting, there was a 5 dB dip at 7 kHz that completely disappeared when
it was flush-mounted. A 5 dB dip means the diffracted sound was only down 7
dB relative to the direct sound. This could really be troublesome. Again, the
message is quite clear: mount all drivers flush with the front panel. As discussed
in the section on my music room,
I eliminated edge diffraction by eliminating the edges. In the last few years
diffraction has begun to receive the attention it deserves, and manufacturers
are rounding edges to reduce diffraction effects. Thanks to Hartmut Vogt for
pointing out the example of the spherical
enclosure designed by Susan Parker. Be aware, though, that rounding edges
only reduces diffraction, it doesn't eliminate it. The terracing introduces
a new set of edges. I tested several design variations. The first design had
the terraced regions in horizontal bands. The edge diffraction from these bands
came straight into the intended "sweet spot" and caused very noticeable ripples
in the frequency response. The chevron-shaped design that can be seen in the
photograph of the front panel (92.5 kb) is
a direct crib from the stealth fighter design. By angling the edges downward,
I directed the sound diffracted from the edges downward into the carpet and
away from the "sweet spot." The slope from one terrace level to another is a
gradual 27-degree incline. This blunts the edges and reduces the diffracted
energy. The combination of these two techniques essentially eliminated diffracted
sound in the vicinity of the "sweet spot."